What is the solution for y^'+y=y^{''} ?

The solution for y^'+y=y^{''} is y=c_{1}e^{-((-1+sqrt(5))t)/2}+c_{2}e^{((1+sqrt(5))t)/2}

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y^'+y=y^{''}

y^{^{'}} + y = y^{^{''}}

y = c_{1} e^{- \frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( 1 + 5 ) t}{2}}

Solution steps

y^{'} (t) + y = y^{''} (t)

Solve linear ODE:

y = c_{1} e^{- \frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( 1 + 5 ) t}{2}}

y = c_{1} e^{- \frac{( - 1 + 5 ) t}{2}} + c_{2} e^{\frac{( 1 + 5 ) t}{2}}

What is the solution for y^'+y=y^{''} ?
The solution for y^'+y=y^{''} is y=c_{1}e^{-((-1+sqrt(5))t)/2}+c_{2}e^{((1+sqrt(5))t)/2}